CN101446634A - Combination measurement method for high precision position, azimuth angle and pitch angle, and device thereof - Google Patents

Abstract

The invention discloses a combination measurement method for high precision position, azimuth angle and pitch angle, and a device thereof; a measurement basic line consists of measurement marking points where two satellite receiving antennas are arranged; a dual-system satellite positioning receiver plate and a beacon receiver plate synchronously receive the signals of a first satellite antenna and a beacon antenna; the dual-system satellite positioning receiver plate synchronously receives the digital signals of the beacon receiver; a GPS receiver plate synchronously receives the signals of a second satellite antenna; the first and second satellite antenna signals and beacon signals are synchronously calculated so as to precisely measure the three-dimensional position where the satellite antenna is arranged and measure the azimuth angle and pitch angle of the antenna basic line under geographic coordinates. The method and the device integrate the dual-system satellite positioning, GPS, beacon receiver plate and computer; the device is provided with a liquid crystal display screen, two satellites and a beacon receiving antenna outside the box, ensures the positioning precision more than 8 meters, receives beacon differential signals at coastal areas, leads the precision to be more than 1 meter and has the directional precision more than 0.1DEG under the basic line of 3 meters.

Description

The combination measurement method of a kind of high precision position, position angle and the angle of pitch and device

Technical field

The invention belongs to the positioning and directing technical field, relate to the combination metering device of a kind of high precision position, position angle and the angle of pitch.

Background technology

Development along with national economy and communication, the positioning and directing technology shows outstanding consequence, especially it is an important component part in armament systems, it is the major equipment that improves self-propelled gun fire accuracy, quick-reaction capability (QRC) and mobility, can penetrate radar, weather radar etc. for self-propelled gun, command car, preceding sight scout car and scouting branch fast accurate position and reference direction are provided, and self-propelled gun is realized in shooting course by resetting from moving.

In order really to accomplish in future war, to preserve oneself effectively, hit the enemy simultaneously again exactly, the motor-driven emission of implementing missile armament has become a development trend of missile operations.Implement the motor-driven emission of guided missile, from the guarantee aspect, a problem that at first will solve is exactly quick location, the orientation of launching site, and its location, the speed of directed velocity and the height of precision will directly influence the speed of the motor-driven emission of guided missile and the effect of hit.Current main positioning and directing technology is divided into two big classes.One class is the inertial positioning directional technology, another kind of global position system (as GPS) the positioning and directing technology that is based on.At present, pursue fast, a high precision important directions of satellite positioning tech research just, experience, the technology of many maturations arranged.

American global positioning system GPS and Muscovite global position system GLONASS provide aspects such as three-dimensional position, three-dimensional velocity and temporal information to bring into play enormous function since successfully using for the user, application also enlarges day by day.GPS and the observed quantity of GLONASS carrier phase are the metrical informations that can reach millimeter level measuring accuracy, and this orientation for armament systems provides powerful technical foundation.Quick location, the orientation that applying GPS or GLONASS measuring technique are carried out launching site has the precision height, equipment is simple, the time is short and unrestricted characteristics, become a kind of means that very likely replace conventional support method.

Begun both at home and abroad at present to adopt GPS to develop and develop positioning and orienting device, but they are generally based on gps system, and number of satellite is limited in the use, can can't locate when being subjected to partial occlusion, and receiver depends on the GP single system, and special circumstances also can can't be worked down.It is main that apparatus of the present invention have adopted the receiver of GPS and Russian GLONASS dual system, simultaneously integrated beacon differential technique, guaranteed that system still works when GPS is influenced, when the coastland, has received the beacon differential signal, can improve real-time positioning precision to 1 meter.

Summary of the invention

In order to solve the problem that the prior art bearing accuracy can't satisfy request for utilization, the purpose of this invention is to provide the combination metering device and the method for a kind of three-dimensional position, position angle and the angle of pitch.

For achieving the above object, the invention provides the combination measurement method of a kind of high precision position, position angle and the angle of pitch, its technical scheme of dealing with problems comprises:

Step 1: utilize the survey mark point at two satellite earth antenna places to constitute the measurement baseline;

Step 2: receive first satellite antenna signals and beacon antenna signal respectively synchronously by dual system satellite positioning receiver plate and beacon receiver plate;

Step 3: dual system satellite positioning receiver plate receives the digital signal of beacon receiver synchronously;

Step 4:GPS receiver card receives second satellite antenna signals synchronously;

Step 5: first satellite antenna signals, second satellite antenna signals and beacon signal are calculated synchronously three-dimensional accurately measurement and the position angle of antenna baseline under geographic coordinate system and the accurate measurement of the angle of pitch that realizes the satellite antenna position.

According to embodiments of the invention, the accurate measurement of described three-dimensional position and position angle, the angle of pitch, be according to coordinate basis transfer principle and coordinate projection conversion principle, three-dimensional position and position angle, the angle of pitch measured are changed between WGS-84 coordinate basis and Beijing 54 coordinate basis, or changed between space and geographical coordinate and Gauss plane coordinate.

According to embodiments of the invention, by observation data synchronous acquisition to dual system satellite positioning receiver plate and GPS receiver card, according to carrier phase data, satellite almanac data, pseudo range data and the doppler data gathered, according to the principle of carrier phase difference, adopt position angle, the angle of pitch bidimensional searching method of taking residual sum of squares (RSS) into account to realize to the position angle of satellite antenna baseline and the real-time measurement of the angle of pitch.

For achieving the above object, the invention provides the combination metering device of a kind of high precision position, position angle and the angle of pitch, the scheme of technical solution problem comprises: GPS+GLONASS dual system satellite positioning receiver plate, GPS receiver card, beacon receiver plate, computing machine carry out integrated, and box is installed LCDs and two satellite earth antennas and a beacon receiving antenna outward;

First end of system's satellite positioning receiver plate and first satellite earth antenna, one end electrically connect, and carry out signal and communication;

Second end of dual system satellite positioning receiver plate and first end of beacon receiver plate electrically connect, and carry out signal and communication;

The 3rd end of dual system satellite positioning receiver plate and first end of computing machine electrically connect, and carry out signal and communication.

Second end of beacon receiver plate and an end of beacon receiving antenna electrically connect, and carry out signal and communication.

First end of GPS receiver card and an end of second satellite earth antenna electrically connect, and carry out signal and communication;

Second end of GPS receiver card and second end of computing machine electrically connect, and carry out signal and communication;

Second end of liquid crystal display and computing machine electrically connects.

According to embodiments of the invention, adopt concentric cable to electrically connect between first end of dual system satellite positioning receiver plate and first satellite earth antenna, one end; Adopt serial ports to electrically connect between second end of dual system satellite positioning receiver plate and the beacon receiver plate; Adopt serial ports to electrically connect between the 3rd end of dual system satellite positioning receiver plate and the computing machine.

According to embodiments of the invention, adopt concentric cable to electrically connect between beacon receiver plate and the beacon receiving antenna.

According to embodiments of the invention, adopt concentric cable to electrically connect between first end of GPS receiver card and second satellite earth antenna, one end; Adopt serial ports to electrically connect between second end of GPS receiver card and the computing machine.

According to embodiments of the invention, described dual system satellite positioning receiver plate and GPS receiver card electrically connect with serial ports respectively.

According to embodiments of the invention, described combination metering device, by the observation data of computing machine synchronous acquisition dual system satellite positioning receiver plate and GPS receiver card, through handling in real time the accurate measurement that realizes the three-dimensional position of satellite antenna and azimuth of director from the gun, the angle of pitch.

According to embodiments of the invention, described combination metering device has adopted system's satellite positioning receiver plate, is used for the three-dimensional position measuring of where distinguishing 8 meters precision of autonomous realization in office; Then receive the GPS difference information in real time according to beacon antenna and beacon receiver plate in the coastland, realize being better than the real time position measurement of 1 meter precision, orientation accuracy is better than 0.1 degree under the situation of 3 meters baselines.

Good effect of the present invention: combination metering device of the present invention, then combine GPS+GLONASS dual system receiver, single system GPS receiver, also integrated beacon receiver, guaranteed that bearing accuracy is better than 8 meters, can receive the beacon differential signal in the coastland, make precision be better than 1 meter, and carry out the calculating of orientation and pitching according to the observation data that two receiver cards receive synchronously, thereby measure the position angle and the angle of pitch, azimuth accuracy is better than 0.1 degree under the situation of 3 meters baselines.

Description of drawings

Fig. 1 is the combination metering device block diagram of high precision position of the present invention, position angle and the angle of pitch

Embodiment

1 couple of the present invention is described in detail below in conjunction with accompanying drawing, is to be noted that described embodiment only is intended to be convenient to the understanding of the present invention, and it is not played any qualification effect.

The present invention adopts satellite positioning tech, realizes the quick measurement to position and position angle, the angle of pitch, has invented the device of a kind of real-time instrumented satellite aerial position and position angle, the angle of pitch.It is the sealed aluminum box of a band liquid crystal display, an integrated PC-104 industrial control computer 7, GPS+GLONASS dual system satellite positioning receiver plate 4, a gps satellite location receiver plate 6 and beacon receiver plate 5 of having fixedly mounted in the aluminium box.Box also has been equipped with first satellite earth antenna 2, second satellite earth antenna 3 and a beacon receiving antenna 1 outward, GPS+GLONASS dual system satellite positioning receiver plate 4 in first satellite earth antenna 2, second satellite earth antenna 3 and the aluminium box, a gps satellite location receiver plate 6 electrically connect, and carry out signal and communication, beacon receiving antenna 1 electrically connects by the beacon receiver plate in concentric cable and the aluminium box 5, and carries out signal and communication.GPS+GLONASS dual system satellite positioning receiver plate 4 and a beacon receiver plate 5 carry out signal and communication by electric connection, realize the three-dimensional position measuring of real-time high-precision.GPS+GLONASS dual system satellite positioning receiver plate 4 and gps satellite location receiver plate 6 all pass through to electrically connect with PC-104 industrial control computer 7, carry out signal and communication, utilize the data of simultaneous observation to realize that three-dimensional position measurement, position angle and the angle of pitch are measured numerical value can carry out Real time dynamic display on LCDs 8 to first satellite earth antenna 2, the position angle of second satellite earth antenna, 3 formations and the real time dynamic measurement of the angle of pitch.

Adopt concentric cable to electrically connect between first end of GPS+GLONASS dual system satellite positioning receiver plate 4 and first satellite earth antenna, 2 one ends; Adopt the RS232 serial ports to electrically connect between second end of GPS+GLONASS dual system satellite positioning receiver plate 4 and the beacon receiver plate 5; Adopt the RS232 serial ports to electrically connect between the 3rd end of GPS+GLONASS dual system satellite positioning receiver plate 4 and the PC-104 industrial control computer 7.

Adopt concentric cable to electrically connect between beacon receiver plate 5 and the beacon receiving antenna 1.

Adopt concentric cable to electrically connect between first end of GPS receiver 6 plates and second satellite earth antenna, 3 one ends; Adopt the RS232 serial ports to electrically connect between second end of GPS receiver card 6 and the PC-104 industrial control computer 7.The serial ports of PC-104 industrial control computer 7 can be exported the location and the directional data of binary-coded decimal form in real time.

GPS+GLONASS dual system satellite positioning receiver plate 4 and beacon receiver plate 5 receive the three-dimensional position that signal that first satellite earth antenna 2, second satellite earth antenna 3 and beacon receiving antenna 1 transmit is accurately measured first satellite earth antenna, 2 positions respectively.Receive the gps carrier phase observations data of gathering synchronously according to GPS+GLONASS dual system receiver card 4 and 6 of GPS receiver cards simultaneously, satellite almanac data, pseudo range data and doppler data, according to the carrier phase data of gathering, satellite almanac data, pseudo range data and doppler data, principle according to the carrier phase difference, the position angle of residual sum of squares (RSS) is taken in employing into account, angle of pitch bidimensional searching method calculates the position angle of baseline in geographic coordinate system and the real-time measurement of the angle of pitch that first satellite earth antenna 2 and second satellite earth antenna 3 constitute in real time by PC-104 industrial control computer 7.

Apparatus of the present invention integrated use GPS+GLONASS dual system satellite positioning tech, GPS location technology, beacon differential technique, the carrier phase difference thought of receiver 4 and receiver 6 has been adopted in combination, realizes the position angle of double antenna baseline and the real-time measurement of the angle of pitch according to the search principle of the position angle and the angle of pitch.

Adopt carrier phase to form two eikonal equations, like this can cancellation ionosphere, parameters such as troposphere, receiver clock correction, make things convenient for data processing.Two eikonal equations are generally:

$\mathrm{\Δ}{\▿\mathrm{\φ}}_{m,b}^{i,j}=\mathrm{\Δ}\▿R_{m,b}^{i,j}+\mathrm{\Δ}\▿N_{m,b}^{i,j}---\left(1\right)$

Wherein:

$\mathrm{\Δ}\▿{\text{\φ}}_{m,b}^{i,j}={\mathrm{\φ}}_m^i-{\mathrm{\φ}}_b^i-{\mathrm{\φ}}_m^j+{\mathrm{\φ}}_b^j,$ Two subtractive combinations for phase place.

$\mathrm{\Δ}\▿{\text{R}}_{m,b}^{i,j}=R_m^i-R_b^i-R_m^j+R_b^j,$ Two subtractive combinations for distance.

$\mathrm{\Δ}\▿{\text{N}}_{m,b}^{i,j}=N_m^i-N_b^i-N_m^j+N_b^j,$ Two subtractive combinations for blur level.

And:

$R_m^i=\sqrt{{(X^i-X_m)}^2+{(Y^i-Y_m)}^2+{(Z^i-Z_m)}^2}---\left(2\right)$

$R_b^i=\sqrt{{(X^i-X_b)}^2+{(Y^i-Y_b)}^2+{(Z^i-Z_b)}^2}---\left(3\right)$

$R_m^i=\sqrt{{(X^j-X_m)}^2+{(Y^j-Y_m)}^2+{(Z^j-Z_m)}^2}---\left(4\right)$

$R_b^i=\sqrt{{(X^j-X_b)}^2+{(Y^j-Y_b)}^2+{(Z^j-Z_b)}^2}---\left(5\right)$

(X ⁱ, Y ⁱ, z ⁱ) be the position of satellite i, resolve (X according to navigation message ^j, Y ^j, Z ^j) be the position of satellite j, also resolve (X according to navigation message _b, Y _b, Z _b) be the position of base station, be known quantity, (X _m, Y _m, Z _m) be the position of rover station, it is amount to be asked.

Key is accurately finding the solution of blur level to utilize two difference carrier phases to find the solution really.The method of much finding the solution blur level is arranged at present, and as based on the searching method of three-dimensional position with based on the searching method of blur level combination, these searching methods generally all are three-dimensional search procedures, and amount of calculation is bigger.For this occasion of precise orientation, the distance of baseline is accurately known, therefore calculate for convenience, save search time, we make full use of the known condition of distance, have adopted the two-dimensional search method based on pitching and orientation, have adopted the method for blur level in the search procedure, the influence of cycle slip can be overcome greatly, and dynamic environment can be adapted to.

Because distance is fixing known between two antennas, therefore just can calculate the increment of coordinate under topocentric coordinates between two antennas according to the position angle and the angle of pitch:

$\left\{\begin{array}{c}{T}_X=b\cos \mathrm{\β}\cos \mathrm{\α}\\ T_Y=b\cos \mathrm{\β}\sin \mathrm{\α}\\ T_Z=b\sin \mathrm{\β}\end{array}\right.---\left(6\right)$

Antenna 1 coordinate in general two antennas is thought known quantity (adopting the single-point positioning result), and should stand as base station, just can calculate according to increment of coordinate, and the coordinate of another antenna (regarding rover station as) can carry out following calculating:

$\{\left[\begin{array}{c}{X}_m\\ Y_m\\ Z_m\end{array}\right]=\left[\begin{array}{ccc}-\sin B\cos L& -\sin L& \cos B\cos L\\ -\sin B\sin L& \cos L& \cos B\sin L\\ \cos B& 0& \sin B\end{array}\right]\left[\begin{array}{c}{T}_X\\ T_Y\\ T_Z\end{array}\right]+\left[\begin{array}{c}{X}_b\\ Y_b\\ Z_b\end{array}\right]---\left(7\right)$

(B is local longitude and latitude position L), and a given prescription parallactic angle and the angle of pitch just can calculate corresponding rover station coordinate.

Adopt following method to calculate for the single frequency receiving ambiguity function is general:

$A=\frac{\underset{k=0}{\overset{l}{\mathrm{\Σ}}}{\left(\underset{i=1,i\≠j}{\overset{n}{\mathrm{\Σ}}}\cos \left[2\mathrm{\π}({\mathrm{\Δ}\▿\mathrm{\φ}}_{\mathrm{im},b}^{i,j}-\mathrm{\Δ}\▿{\widetilde{\mathrm{\φ}}}_{m,b}^{i,j})\right]\right)}_k}{k*(n-1)}---\left(8\right)$

Wherein, Be two difference observed readings of utilizing carrier phase to calculate.

And:

Be two poor, promptly according to the distance of base station position, rover station position calculation

$\mathrm{\Δ}\▿{\widetilde{\mathrm{\φ}}}_{m,b}^{i,j}={\tilde{R}}_m^i-R_b^i+{\tilde{R}}_m^j-R_b^j,$ Specifically calculate with top formula.K represents counting epoch, and i represents to defend asterisk, and j is the reference satellite of two differences, and n is the satellite number.

On the tram, ambiguity function A has maximum value, and near 1.But for single epoch, the pairing blur level maximum value of single two differences is not unique.Therefore in the practical application, usually join together to calculate together with all two difference ambiguity functions of several epoch earlier, remain the maximum value except ambiguity function on the tram like this, the possibility that occurs maximum value on other aspect will gradually reduce.

During concrete the search, can in the hunting zone, carry out two-dimensional search earlier by the step-size in search of 0.5 degree interval as the position angle and the angle of pitch.After calculating corresponding rover station position, calculate ambiguity function greater than all extreme points of certain threshold value (as 0.85) as check point, (in ± 0.5 degree scope) carries out the maximum point search of long 0.01 degree of small step near these check points again, obtains pairing position of maximum blur level functional value and position angle, the angle of pitch.

During apparatus of the present invention work, utilize the survey mark point at two satellite earth antenna places to constitute the measurement baseline; First satellite earth antenna 2 and second satellite earth antenna 3 are fixedly mounted on the object of wanting measuring position and position angle, the angle of pitch, and accurately measure distance between first satellite earth antenna 2 and second satellite earth antenna 3 in advance, be accurate to millimeter.Adopt concentric cable that first satellite earth antenna 2 and second satellite earth antenna 3 and beacon receiving antenna 1 are connected on the corresponding interface of combination metering device.

GPS+GLONASS dual system satellite positioning receiver plate 4 receives GPS and the GLONASS satellite-signal that satellite earth antenna 1 transmits by concentric cable, beacon receiver plate 5 concentric cable receive the beacon signal that beacon antenna 1 transmits, and send beacon signal to GPS+GLONASS dual system receiver card 4 by serial ports, after handling, GPS+GLONASS dual system receiver card 4 again information is passed to PC-104 industrial control computer 7 by serial ports.GPS receiver card 6 receives the gps satellite signal that second satellite earth antenna 3 transmits by concentric cable, and passes to PC-104 industrial control computer 7 by serial ports.PC-104 industrial control computer 7 calculates three-dimensional position in real time according to the information that GPS+GLONASS dual system receiver card 4 transmits, in officely where distinguish the location that to realize 8 meters precision, and can realize being better than 1 meter hi-Fix according to the difference information that beacon transmits in the coastland.PC-104 industrial control computer 7 is according to the observation data of the GPS+GLONASS dual system receiver card 4 that receives synchronously and the observation data of GPS receiver card 6 simultaneously, adopt carrier phase difference thought, use the position angle and the angle of pitch that position angle angle of pitch bidimensional searching method calculates first satellite earth antenna 2 and second baseline that satellite earth antenna 3 constitutes in real time.

Measured three-dimensional position and results such as position angle, the angle of pitch can be according to principle of coordinate transformation, operate by soft-key button, position and azimuth pitch information can be changed between WGS-84 coordinate basis and Beijing 54 coordinate basis in real time, also can carry out the mutual conversion between space and geographical coordinate and the Gauss projection coordinate, the result of measurement can show current correct time, geographical longitude and latitude and height and two position angles that satellite antenna constituted and the angles of pitch in real time on liquid crystal display 8.

The above; only be the embodiment among the present invention; but protection scope of the present invention is not limited thereto; anyly be familiar with the people of this technology in the disclosed technical scope of the present invention; can understand conversion or the replacement expected; all should be encompassed in of the present invention comprising within the scope, therefore, protection scope of the present invention should be as the criterion with the protection domain of claims.

Claims (10)

1, the combination measurement method of a kind of high precision position, position angle and the angle of pitch is characterized in that, comprises that step is as follows:

Step 1: utilize the survey mark point at two satellite earth antenna places to constitute the measurement baseline;

Step 2: receive first satellite antenna signals and beacon antenna signal respectively synchronously by dual system satellite positioning receiver plate and beacon receiver plate;

Step 3: dual system satellite positioning receiver plate receives the digital signal of beacon receiver synchronously;

Step 4:GPS receiver card receives second satellite antenna signals synchronously;

Step 5: first satellite antenna signals, second satellite antenna signals and beacon signal are calculated synchronously three-dimensional accurately measurement and the position angle of antenna baseline under geographic coordinate system and the accurate measurement of the angle of pitch that realizes the satellite antenna position.

2, combination measurement method according to claim 1, it is characterized in that, the accurate measurement of described three-dimensional position and position angle, the angle of pitch, be according to coordinate basis transfer principle and coordinate projection conversion principle, three-dimensional position and position angle, the angle of pitch measured are changed between WGS-84 coordinate basis and Beijing 54 coordinate basis, or changed between space and geographical coordinate and Gauss plane coordinate.

3, combination metering device according to claim 1, it is characterized in that, by observation data synchronous acquisition to dual system satellite positioning receiver plate and GPS receiver card, according to carrier phase data, satellite almanac data, pseudo range data and the doppler data gathered, according to the principle of carrier phase difference, adopt position angle, the angle of pitch bidimensional searching method of taking residual sum of squares (RSS) into account to realize to the position angle of satellite antenna baseline and the real-time measurement of the angle of pitch.

4, the combination metering device of a kind of high precision position, position angle and the angle of pitch, be characterised in that, comprise: dual system satellite positioning receiver plate, GPS receiver card, beacon receiver plate, computing machine carry out integrated, and box is installed LCDs and two satellite earth antennas and a beacon receiving antenna outward;

First end of dual system satellite positioning receiver plate and first satellite earth antenna, one end electrically connect, and carry out signal and communication;

Second end of dual system satellite positioning receiver plate and first end of beacon receiver plate electrically connect, and carry out signal and communication;

The 3rd end of dual system satellite positioning receiver plate and first end of computing machine electrically connect, and carry out signal and communication;

Second end of beacon receiver plate and an end of beacon receiving antenna electrically connect, and carry out signal and communication;

First end of GPS receiver card and an end of second satellite earth antenna electrically connect, and carry out signal and communication;

Second end of GPS receiver card and second end of computing machine electrically connect, and carry out signal and communication;

Second end of liquid crystal display and computing machine electrically connects.

5, combination metering device according to claim 4 is characterized in that, adopts concentric cable to electrically connect between first end of dual system satellite positioning receiver plate and first satellite earth antenna, one end; Adopt serial ports to electrically connect between second end of dual system satellite positioning receiver plate and the beacon receiver plate; Adopt serial ports to electrically connect between the 3rd end of dual system satellite positioning receiver plate and the computing machine.

6, combination metering device according to claim 4 is characterized in that, adopts concentric cable to electrically connect between beacon receiver plate and the beacon receiving antenna.

7, combination metering device according to claim 4 is characterized in that, adopts concentric cable to electrically connect between first end of GPS receiver card and second satellite earth antenna, one end; Adopt serial ports to electrically connect between second end of GPS receiver card and the computing machine.

8, combination metering device according to claim 4 is characterized in that, described dual system satellite positioning receiver plate and GPS receiver card electrically connect with serial ports respectively.

9, combination metering device according to claim 4, it is characterized in that, by the observation data of computing machine synchronous acquisition dual system satellite positioning receiver plate and GPS receiver card, through handling in real time the accurate measurement that realizes the three-dimensional position of satellite antenna and azimuth of director from the gun, the angle of pitch.

10, the combination metering device of a kind of high precision position, position angle and the angle of pitch has adopted dual system satellite positioning receiver plate, is used for the three-dimensional position measuring of where distinguishing 8 meters precision of autonomous realization in office; Then receive the GPS difference information in real time according to beacon antenna and beacon receiver plate in the coastland, realize being better than the real time position measurement of 1 meter precision, orientation accuracy is better than 0.1 degree under the situation of 3 meters baselines.

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